The computational complexity and efficiency of the approximate mode component synthesis (ACMS) method is investigated for the two-dimensional heterogeneous Helmholtz equations, aiming at the simulation of large but finite-size photonic crystals. The ACMS method is a Galerkin method that relies on a non-overlapping domain decomposition and special basis functions defined based on the domain decomposition. While, in previous works, the ACMS method was realized using first-order finite elements, we use an underlying hp–finite element method. We study the accuracy of the ACMS method for different wavenumbers, domain decompositions, and discretization parameters. Moreover, the computational complexity of the method is investigated theoretically and compared with computing times for an implementation based on the open source software package NGSolve. The numerical results indicate that, for relevant wavenumber regimes, the size of the resulting linear systems for the ACMS method remains moderate, such that sparse direct solvers are a reasonable choice. Moreover, the ACMS method exhibits only a weak dependence on the selected domain decomposition, allowing for greater flexibility in its choice. Additionally, the numerical results show that the error of the ACMS method achieves the predicted convergence rate for increasing wavenumbers. Finally, to display the versatility of the implementation, the results of simulations of large but finite-size photonic crystals with defects are presented.

Although enterprises in the informal food sector require energy to transform, cook and process food, energy-use patterns in this sector are not well understood by policymakers and the local-level authorities who regulate their trading activities. This paper reviews relevant literature and presents empirical data collected in Rwanda, Senegal and South Africa on the use of traditional and modern energy sources by informal food sector operators. Our sample includes male- and female-operated enterprises in the urban centres of three African countries where the informal food sector is important, not only for providing the convenience of affordable and readily prepared meals, but also as a source of income for women and men in developing countries. Multiple fuel-use and energy-stacking strategies are common among informal food enterprises and policy needs to acknowledge this if it is to intervene in ways that will benefit both enterprises and regulators.